Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
bool binaria(vector<int> &valores, int buscar) {
  int left = 0, right = valores.size() - 1;
  while (left <= right) {
    int middle = (left + right) / 2;
    if (valores[middle] == buscar) {
      return true;
    }
    if (valores[middle] < buscar)
      left = middle + 1;
    else
      right = middle - 1;
  }
  return false;
}
int main() {
  std::ios_base::sync_with_stdio(0);
  cin.tie(0);
  int n, aux;
  cin >> n;
  vector<int> valores;
  for (int i = 1; i < n; ++i) {
    aux = (i * (i + 1)) / 2;
    if (aux >= n) break;
    valores.push_back(aux);
  }
  for (int i = 0; i < valores.size(); ++i) {
    if (binaria(valores, n - valores[i])) {
      cout << "YES" << endl;
      return 0;
    }
  }
  cout << "NO" << endl;
  return 0;
}